Formalism of Nonequilibrium Perturbation Theory and Kondo Effect

TL;DR

This paper develops a rigorous real-time perturbation theory formalism for nonequilibrium systems, clarifying the relationship with imaginary-time methods and ensuring proper self-energy derivation.

Contribution

It provides a new real-time perturbative approach based on the adiabatic theorem, resolving foundational issues and connecting with existing imaginary-time formalisms.

Findings

Self-energies as functions in time are properly defined.

Exact agreement with imaginary-time perturbative functions.

Formalism can be generalized to broader applications.

Abstract

The formalism of nonequilibrium perturbation theory was constructed by Schwinger and Keldysh and then was developed with the diagrammatical technique by Lifshitz and Pitaevskii. Until now there has been widespread application to various researches in physics, condensed matter, plasmas, atoms and molecules, nuclear matter etc.. In spite of this, the formalism has not been established as perturbation theory. For example, there is no perturbative method to derive arbitrary self-energy properly. In addition, the connection with other formalism, e.g., the Matsubara imaginary-time perturbative formalism is uncertain. Although there must be the relationship between self-energies in the perturbative formalism, such basic problems remain to be solved. The solution is given by the present work. The real-time perturbative expansion is performed on the basis of the adiabatic theorem. As the results, the requirements of self-energies as functions in time are demonstrated and the formulated self-energies meet the known relations. Besides, it gives exact agreement with functions derived by perturbative expansion in imaginary-time and analytical continuity. As a consequence, it implies that the present formalism can be generalized.